Airfoil trailing edge

ABSTRACT

An aerofoil wing comprising upper and lower surfaces meeting at the leading and trailing edges and a camber line representing the curvature of the aerofoil comprising at least two regions of substantially linear increases in curvature and wherein the increases in curvature are of monotonically increasing magnitude. Preferably there are three regions of substantially linear increases in curvature.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates to aerofoil sections and in particular to thosedesigned to endure turbulent i.e. high Reynolds number air flows. It hasparticular application to large civil aircraft.

2. Discussion of Prior Art

It is an ever present desire to design aerofoils having improved dragcharacteristics which at the same time do not diminish liftcharacteristics to an undesirable level. The parasitic drag on anaircraft includes both viscous drag, resulting from the viscosity of theair, and pressure drag, resulting from an imbalance of pressure actingon the aircraft surfaces. At subsonic velocity the viscous drag is thepredominant contributor to the parasitic drag of the aircraft. However,as the aircraft approaches Mach 1.0, local regions of supersonic flowdevelop on the surface of the aircraft. For local Mach numbers nearlyequal to 1.0, the air is able to recompress (return to subsonicconditions) without forming local pressure jump discontinuities orshocks on the surface of the aircraft. U.S. Pat. No. 5,318,249 describesa transonic aerofoil in which the absolute value of the negative slopeof the camber increases by at least about 50% over the aft 4% of thechord.

It is an object of the invention to provide an aerofoil with evenfurther improved reduced drag characteristics than prior art aerofoils.

SUMMARY OF THE INVENTION

The inventors have determined that applying a pressure distribution onthe upper surface of an aerofoil with a mild adverse pressure gradientrecovery, followed by a rapid increase in pressure just short of thetrailing edge, allows aerofoils to be designed which offer lower drag athigh Reynolds numbers. The effect of this is to maximise lift to dragratio by pushing the boundary layer as hard as possible i.e. close toseparation. The inventors have defined a series of upper surfacepressure distributions made up of regions of zero pressure gradient,regions of equilibrium, adverse gradient and jumps in pressure. Byapplying a simplified boundary-layer calculation to the upper surfacepressure distributions the inventors have showed that improvements inlift to drag ratios are possible over prior art aerofoils. The inventorshave also determined that there was a value of adverse pressure gradientparameter above which the flow would be sensitive to Reynolds number.

In accordance with the present invention an aerofoil wing comprisesupper and lower surfaces meeting at the leading and trailing edges and acamber line representing the curvature of the aerofoil characterised inthat the camber line comprises at least two regions of substantiallylinear increases in curvature; wherein in a first region the maximumdeviation of linearity in curvature increase from a straight line overat least 20% of chord is 1/chord; wherein in a second region includes acurvature increase of at least 3/chord the maximum deviation oflinearity in curvature increase is 1.5/chord from a straight line; andwherein the increases in curvature are of monotonically increasingmagnitude.

BRIEF DESCRIPTION OF THE FIGURES

The invention will be described with reference to the following figuresof which:

FIG. 1 shows a figure of the desired pressure distribution resultingfrom flow over an aerofoil according to the invention.

FIGS. 2a and 2 b show a design of an aerofoil according to the inventionin comparison with a conventional aerofoil.

FIG. 3 shows a comparison of surface slope of a conventional aerofoiland one according to the invention.

FIGS. 4a-j show various embodiments of the aerofoils according to theinvention in terms of the curvature of camber.

FIG. 5 shows a generalised representation of the aerofoils of FIG. 4 interms of camber curvature.

FIG. 6 compares the half thickness distribution for a conventionalaerofoil and two airfoils embodying the invention.

FIGS. 7, 8, 9, 10 each show graphs of drag coefficient against liftcoefficient for two aerofoils according to the invention and incomparison with a conventional aerofoil for Mach numbers 0.74 and 0.77respectively.

DETAILED DISCUSSION OF EMBODIMENTS

FIG. 11 compares the drag rise boundary for a conventional aerofoil andtwo aerofoils according to the invention.

FIG. 1 shows the desired pressure distribution over an aerofoil asdetermined by the inventors in order to reduce drag at high Reynoldsnumbers. The upper aerofoil surface 1 pressure distribution consists ofa “sonic” or flat roof top, AB, followed by a mild adverse pressurerecovery, BC, which is terminated by a rapid pressure rise, CD. Theshape of the aerofoil in the region of AB is constrained to some extentby the need for good supercritical flow development as indicated by thedashed line. The chordwise position of B can vary from 5% to 90% chord.The location of the start of the pressure rise C is at about 98.5% ofchord. The rise in pressure coefficient at the rapid pressure jump, CD,has been varied from 0 up to 0.465; the magnitude is chosen to avoid arapid rise in viscous drag. However for some particular applications itmight be advantageous to allow for a higher value. The lower aerofoilsurface 2 features a favourable pressure gradient A′B′, followed by amild adverse pressure recovery B′C′, and terminated by a rapidacceleration C′D. The position of B′ is determined by location of themaximum thickness of the aerofoil section. Variations on the lowersurface design are also illustrated on the sketch, showing. aconventional rear loading and local rear loading. The purpose of thelocal rear loading is to reduce the aerofoil trailing edge angle inorder to minimise the risk of increasing the viscous drag level. Therapid acceleration C′D, reduces the value of the boundary layer momentumthickness following the growth in the region of the lower surfacepressure recovery.

Before the embodiments of the aerofoils according to the invention aredescribed it is necessary to define some terms. The term “camber line”is the line defining the mid point between the upper and lower surfacesof the aerofoil extending from the leading to the trailing edge i.e.z_(camber) (camber line)=(z_(upper)+z_(lower))/2 where z is the verticallocation of the surface at a particular chord position.

The term slope A is defined as dz/dx; and the term curvature k isdefined as dA/ds (d²z_(camber)/dx²)/((l+(z_(camber)/dx)²) where x is isthe chordwise location made non-dimensional by chord length. A is theslope of the camber line at chordwise position x, and s is the distancealong the camber line.

FIG. 2 a shows an example of an aerofoil according to the invention incomparison with a conventional aerofoil 4 shown in broken lines on thefigure. FIG. 2b shows in more detail the aft portion of this aerofoil.The section of trailing edge of the novel aerofoil shows a substantialincrease camber aft of 97% of chord. However in order to understand theinvention it is more appropriate to describe the invention by looking atthe slope of the camber.

FIG. 3 compares the slope of camber of a known prior art aerofoil 5 andone according to the invention 6 having a reduced level of slope between50% and 78% of chord followed by an increase in negative slope over theaft 3% of chord. The increase in negative slope at the trailing edge isof the order approaching three times the value at 97% chord of the priorart aerofoil. The negative camber of the novel section increases from−0.175 to about −0.50 at the trailing edge.

FIGS. 4a to 4 j show the curvature against chord position for tenexamples of aerofoils which fall within the scope of the invention.

FIG. 5 shows a generalised representation of these figures showing threedistinct regions of linear negative increase in curvature in the rearhalf of the aerofoil chord. Thus each aerofoil according to theinvention can be described as having three distinct slopes ofmonotonically linearly increasing negative changes in curvature. Thefirst region 7 comprises generally a shallow linear increase in negativecurvature as is shown from chord position a to b, the second region 8 amore steep linear increase in curvature from c to d and the third region9 an even steeper increase in curvature from e to f.

The table below gives further information from the curvaturecharacteristics of the aforementioned examples with particular referenceto the three regions 7, 8, 9 of linear increase in curvature asdescribed above. The table gives the magnitude of curvature ofcamberline at the start and finish of the first (a-b), second (c-d), andthird (e to f) regions respectively, as well as the chord positions ofthe start and finish of these regions. The symbol λ denotes the [slope]change in curvature of the camberline [at the finish of each regionmultiplied by 100] per unit chord.

Slope 1 Slope 2 Slope 3 x/c x/c x/c x/c x/c x/c Aerofoil a κ b κ λ/100 cκ d κ λ/100 e κ f κ λ/100 a 0.650 −0.1 0.960 −1.0 −0.029 0.95 −2.0 0.980−8.4 −4.92 0.990 −9.0 0.998 −21.0 −15.0 b 0.680 −0.3 0.960 −1.0 −0.0250.965 −1.0 0.980 −7.7 −4.46 0.990 −8.5 0.998 −13.9 −6.75 c 0.630 −0.20.980 −0.5 −0.009 0.980 −0.5 0.990 −19.0 −18.50 0.990 −19.0 0.998 −45.0−32.5 d 0.65 −0.2 0.963 −1.0 −0.020 0.980 −0.5 0.990 −21.0 −20.50 0.990−21.0 0.998 −44.0 −28.75 e 0.65 0.0 0.95 −1.0 −0.033 0.980 −2.0 0.985−16.0 −28.00 0.990 −20.0 0.998 −57.0 −46.25 f 0.750 −0.6 0.960 −1.0−0.019 0.965 −1.4 0.980 −8.0 −4.40 0.990 −8.0 0.998 −20.5 −15.63 g 0.750−0.4 0.960 −0.8 −0.019 0.960 −0.8 0.995 −9.4 −2.46 0.995 −9.4 0.999−23.0 −34.0 h 0.650 −0.1 0.960 −1.3 −0.040 0.965 −2.0 0.980 −8.0 −4.000.990 −8.0 0.998 −19.0 −13.8 i 0.650 −0.2 0.950 −1.35 −0.038 0.965 −1.350.985 −9.0 −3.82 0.990 −10.0 0.998 −28.8 −23.5 j 0.770 −0.7 0.960 −1.0−0.043 0.965 −1.0 0.980 −4.0 −2.00 0.990 −1.0 0.998 −4.0 −3.75

The table above shows for each aerofoil section the start and end pointsin terms of percentage chord of each region 7, 8, 9 as well as thecurvature at these points. As can be seen the first region of linearincreasing curvature extends over a large proportion of the camber linefrom generally 65% chord to approximately 95% chord. The increase innegative curvature is fairly shallow and the curvature increases overthis region by an amount between 0.3 and 1.2. The second increase innegative curvature is generally over from the range 95 to 98% chord to98 to 99% chord and is a sharper increase in the region of 3 to 20.5.The third increase in negative curvature takes place generally in thelast 1% of chord from 99% chord and is a further increase ranging from 3to 37.

FIG. 6 compares the half thickness distribution zt/c, for a conventionalaerofoil A and two aerofoils C and B according to the invention, where“c” is the section/wing chord and “t” is section/wing thickness.Aerofoil A has an upper surface pressure distribution with aconventional lower surface rear loading. Aerofoil B has a mild lowersurface adverse pressure recovery with the local rear loading. Thefigures show that the aerofoils C and B have a significant increase inwing box volume, particularly between from 50% to about 95% of chord.The difference in wing box volume at 65% of chord are 20% and 30% largerfor aerofoils C and B respectively compared to the conventionalaerofoil. For aerofoil B the difference between the conventionalaerofoil is even more pronounced at 80% of chord having a value of zt/cof about 0.024 and at 87% of chord this value is 0.017 compared withless than 0.01 for the conventional aerofoil; this is about 70% increasein wing box volume. The increase in rear depth offers better flapdesigns for low speed performance, lower structural weight and increasedfuel volume. Therefore, a novel design based on aerofoil B can beexploited to trade lift for an increase in depth and maintain anacceptable aerodynamic performance.

FIGS. 7, 8, 9, 10 are graphs of drag coefficient against liftcoefficient for two novel trailing-edge aerofoils 10, 11 respectively atMach numbers 0.74 and 0.77 respectively. Both novel aerofoils are uppersurface designs with differences in the start of the pressure recovery.The start of the pressure recovery is 70% chord for novel aerofoil 10and 65% chord for novel aerofoil 11. Generally, the drag levels aresimilar to those for the conventional aerofoil, with the novel aerofoil10 showing a slight drag penalty and novel aerofoil 11 a slight dragreduction at Mach 0.74. The design of novel aerofoil 10 gives a higherlift coefficient and has a lower drag at 0.9 C_(L) for Reynolds numbersof 40×10⁶ and 60×10⁶. For Mach 0.77, both novel aerofoils show a benefitin terms of reduced drag relative to the conventional section.

FIG. 11 shows the improvement in drag rise boundary over a range ofcivil transport wings comparing novel aerofoil 10, novel aerofoil 11,and a conventional aerofoil. Novel aerofoil 11 has the same uppersurface pressure distribution as novel aerofoil 10, but with a mildlower surface adverse pressure recovery with local rear loading close tothe trailing edge. Novel aerofoil 11 has traded lift for an increase inthickness over the rear portion of the section. The results show a smalldrag penalty for novel aerofoil 11 relative to novel aerofoil 10.

The invention covers an aerofoil comprising upper and lower surfacesmeeting at the leading and trailing edges and having a chord lineextending from said leading and trailing edges and a camber linerepresenting the curvature of the aerofoil, wherein aft of 50% chord thecamber line has three substantially linear increases in negative cambercurvature. The examples given in the figures clarify this claim. Inorder to define the three regions of substantially linear increase incurvature it is necessary to make some definition.

These linear regions are defined as extending over either 20% of chordor covering a curvature increase of at least 3. It is therefore intendedto exclude small increases in negative camber curvature which extendover a small portion of chord length. Additionally the term linear needsto be defined. The term linear for the first region is defined aswherein the maximum deviation in curvature from a straight line drawnalong the region over at least 20% of chord is 1. The term linear forboth the second and third regions is defined as wherein the maximumdeviation in curvature is 1.5 from a straight line drawn along theregion over at least an increase of +/−3.

The term linear for both the second and third regions is defined aswherein the maximum deviation in curvature is +/−1.5 from a straightline drawn along the region over at least an increase of [+/−]3.

What is claimed is:
 1. A supercritical airfoil, said airfoil havingupper and lower surfaces meeting at leading and trailing edges and achord defined as the distance between said leading and trailing edges,said airfoil having a camber line representing the locus of pointsequidistant between the upper and lower surfaces along the chord, saidairfoil camber line comprised of at least two regions as follows: afirst region, extending over at least 20% of said airfoil chord, inwhich said camber line is curved with said curvature increasingly curvedat a first generally constant rate, where any deviation from a linearincrease in curvature of said camber line along said first region isless than 1/chord; and a second region in which said camber line iscurved with said curvature increasingly curved at a second generallyconstant rate greater than said first generally constant rate, saidsecond region having a maximum curvature at least 3/chord greater thanthe maximum curvature of said first region, where any deviation from alinear increase in curvature of said camber line along said secondregion is less than 1.5/chord.
 2. An aerofoil as claimed in claim 1wherein there are three regions of substantially linear increases incurvature (7, 8, 9).
 3. An aerofoil as claimed in claim 2, wherein thethree regions of substantially linear increases in curvature are aft of50% chord.
 4. An aerofoil as claimed in claim 1 having a firstsubstantially linear increase in curvature over the region of between 60and 77% to between 96 to 98% chord.
 5. An aerofoil as claimed in claim4, wherein said first linear increase in curvature is between 0.2 and−1.4.
 6. An aerofoil as claimed in claim 1 having a second substantiallylinear increase in curvature over the region of between 95.0 to 98.0% tobetween 98 to 99.5% chord.
 7. An aerofoil as claimed in claim 6, whereinthe second said linear increase in curvature is between −3 and −30. 8.An aerofoil as claimed in claim 1 having a third substantially linearincrease in curvature over the region of between 99 to 99.5% to about99.9% chord.
 9. An aerofoil as claimed in claim 8, wherein the thirdlinear increase in curvature is between −3 and −40.